I feel responsible.
Why? Seriously - you need to find an answer to this question.
Why do you feel responsible for the relationship between two adults? Look at your own parents and your upbringing - who made you feel like you had to be responsible for other people's relationships?
I think you need to go to counselling to explore this in depth.
I don't want to be the one to ignore her texts
You won't be 'the one' as DH is also ignoring her texts. So that is two of you doing the ignoring. It is your duty as his wife to follow his lead in this.
If you mean that you will feel bad about yourself for ignoring someone's texts, then have a good think about why this is. Why won't you give yourself permission to ignore someone?
Can you just let yourself feel bad and put up with that discomfort?
Would it damage your self-image too much to do a "bad" thing like ignoring someone? Why do you have to be 'the good person'?
I don't want to be the one who is getting in the way of them having a relationship
It is very odd that you see opting out of the situation by ignoring her as "getting in the way". Quite the opposite, ignoring her would be getting out of the way, leaving the two of them to have their relationship on their own terms.
You feel that ignoring her is a deliberate act of you damaging their relationship. This is very twisted thinking.
Your starting point seems to be that you are meant to make everyone else happy, to help everyone else, and if you refuse then that makes you the one at fault. This is not a healthy way to think and feel.
So I feel an obligation to respond.
This is what you need to change. If you insist on carrying on "being the good person" who doesn't ignore her, it will just lead to irreparable damage to you, your baby, and your marriage.
As I said before, your duty is to follow your husband's lead in this. If he is happy to ignore her, so should you.
It is NOT a healthy thing for you to decide to do things your way, because seeing yourself as a "bad" person makes you feel bad.